Acknowledgements
The material acknowledged below is Proprietary (see terms and conditions) and used under licence (not subject to Creative Commons licence).The content is from SM358_1 Book 1 Wave Mechanics– Chapter 7...
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6 Summary
Session 1Scattering is a process in which incident particles interact with a target and are changed in nature, number, speed or direction of motion as a result. Tunnelling is a quantum phenomenon in...
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5.4 The scanning tunnelling microscope
The scanning tunnelling microscope (STM) is a device of such extraordinary sensitivity that it can reveal the distribution of individual atoms on the surface of a sample. It can also be used to...
View Article5.3 Stellar astrophysics
If tunnelling out of nuclei is possible then so is tunnelling in! As a consequence it is possible to trigger nuclear reactions with protons of much lower energy than would be needed to climb over the...
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5.2 Alpha decay
You have probably met the law of radioactive decay, which says that, given a sample of N0 similar nuclei at time t = 0, the number remaining at time t is N(t) = N0e−λt, where λ, the decay constant for...
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The discovery that quantum mechanics permits the tunnelling of particles was of great significance. It has deep implications for our understanding of the physical world and many practical applications,...
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4.4 Stationary states and tunnelling in one dimension
We will now use the stationary-state approach to analyse the tunnelling of particles of energy E0 through a finite square barrier of width L and height V0 when E0< V0 (see Figure 21). Figure 21 A...
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4.3 Stationary states and barrier penetration
The example of tunnelling we have just been examining can be regarded as a special case of scattering; it just happens to have E0< V0. As long as we keep this energy range in mind, we can apply the...
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4.2 Wave packets and tunnelling in one dimension
Figure 18 shows a sequence of images captured from a wave packet simulation program. The sequence involves a Gaussian wave packet, with energy expectation value 〈E〉 = E0, incident from the left on a...
View Article4.1 Overview
One of the most surprising aspects of quantum physics is the ability of particles to pass through regions that they are classically forbidden from entering. This is the phenomenon of quantum-mechanical...
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3.6 Scattering in three dimensions
Sophisticated methods have been developed to analyse scattering in three-dimensions. The complexity of these methods makes them unsuitable for inclusion in this unit but it is appropriate to say...
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3.5 Scattering from finite square wells and barriers
The procedure used to analyse scattering from a finite square step can also be applied to scattering from finite square wells or barriers, or indeed to any combination of finite square steps, wells and...
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3.4 Probability currents
The expressions we have derived for reflection and transmission coefficients were based on the assumption that the intensity of a beam is the product of the speed of its particles and their linear...
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3.3 Scattering from a finite square step
The kind of one-dimensional scattering target we shall be concerned with in this section is called a finite square step. It can be represented by the potential energy functionThe finite square step...
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3.2 Stationary states and scattering in one dimension
The key idea of the stationary-state approach is to avoid treating individual particles, and to consider instead the scattering of a steady intense beam of particles, each particle having the same...
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3.1 Overview
Scattering calculations using wave packets are so laborious that they are generally done numerically, using a computer. However, in many cases, scattering phenomena can be adequately treated using a...
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2.2 Wave packets and scattering in one dimension
Figure 6 shows the scattering of a wave packet, incident from the left, on a target represented by a potential energy function of the formPotential energy functions of this type are called finite...
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2.1 Overview
Session 2 discusses the scattering of a particle using wave packets. We shall restrict attention to one dimension and suppose that the incident particle is initially free, described by a wave packet of...
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1 What are scattering and tunnelling?
The phenomenon of scattering was an important topic in physics long before the development of wave mechanics. In its most general sense, scattering is a process in which incident particles (or waves)...
View ArticleLearning outcomes
By the end of this unit you should be able to:explain the meanings of the emboldened terms and use them appropriately;describe the behaviour of wave packets when they encounter potential energy steps,...
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